Roman Chapko

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We consider the initial boundary value problem for the heat equation in a region with in nite and nite boundaries (direct problem) and the related problem to reconstruct the nite boundary from Cauchy data on the in nite boundary (inverse problem). The numerical solution of the direct problem is realized by a boundary integral equation method. For an(More)
A direct boundary integral equation method for the numerical construction of harmonic functions in threedimensional layered domains containing a cavity Roman Chapko a , B. Tomas Johansson b & Olena Protsyuk a a Faculty of Applied Mathematics and Informatics , Ivan Franko National University of Lviv , 79000 , Lviv , Ukraine b School of Mathematics ,(More)
We consider two types of inverse boundary problems related to the Laplace equation in planar double connected domains. The first one consists in the determining the Cauchy data on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the function (or the normal derivative) is known and, additionally, on a portion of(More)
On the interpolation of a function on a bounded domain by its traces on parametric hypersurfaces Roman Chapko, Christina Babenko, Volodymyr Khlobystov & Volodymyr Makarov a Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Lviv, Ukraine b Ukrainian Engineering Pedagogics Academy, Kharkiv, Ukraine c Institute of(More)
In this paper we describe a fully discrete quadrature method for the numerical solution of a hypersingular integral equation of the rst kind for the scattering of time-harmonic elastic waves by a cavity crack. We establish convergence of the method and prove error estimates in a HH older space setting. Numerical examples illustrate the convergence results.
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